M. M. Panja

The Dalgarno - Lewis method as a perturbation theory

The Dalgarno - Lewis summation technique as used in the Rayleigh - Schrodinger perturbation theory is examined. It is shown that this technique forms an independent perturbation theory and can be used to deal with both bound- and continuum-state problems with some added advantage over other such approaches.

1/η expansion for the binding energies of finite-depth potentials

Abstract We present a systematic perturbative method for calculating the binding energies of ro-vibrational quantum states for a finite depth potential. Using an asymptotic expansion in powers of 1/η, where η is the dimensionless physical depth parameter, explicit calculations are performed. Our analytic results lead to highly convergent series for the binding energies, and numerical results for realistic potentials such as Morse and Lennard-Jones potentials are found to be in excellent agreement with the exact ones.

Application of the shifted large‐N method to the rovibrational spectroscopy of diatomic molecules

Computations of energy levels, expectation values of various powers of internuclear separation, and Franck–Condon factors for molecular potentials have been carried out within the framework of shifted large‐N technique. In contrast to other perturbative as well as semiclassical calculations, we obtain compact analytic expressions for these quantities. For illustration, our predicted results for perturbed Kratzer potential are compared with those derived by numerical integration. The method gives quite accurate results for a wide range of rovibrational quantum numbers. Further possible applications, in particular, to Morse oscillators are finally discussed.

Shifted large-N expansion for the power-law potentials in the Klein-Gordon equation with applications

Analytic expressions for the spectrum and the wavefunction resulting from the relativistic generalisation of the shifted large-N expansion method as applied to the general power-law potentials V(r)=B+Arv are presented. These expressions obtained in the context of the Klein-Gordon equation are then used to compute the mass spectra and leptonic decay widths of mesonic states composed of heavy quarks. The relativistic corrections are found to be in good agreement with those obtained by elaborate analytic (WKB) and numerical methods. Compact analytic results of the shifted large-N expansion for relativistic systems are seen to be applicable to a much wider class of problems than are most other approximation methods.

Geometric phase from a combined evolution‐operator‐invariant technique

The quantum phase problem is investigated by a synthesis of the evolution operator technique and method of invariants. This approach has been found to be quite effective to disclose interrelationship between geometric phases differing in the nature of evolution and to obtain results for them without invoking the concept of parallel transport in the projective Hilbert space. The usefulness of the method developed is ascertained by studying the geometric phases associated with spinor evolutions in rotating magnetic field.

ISOSPECTRAL INTERACTIONS FOR THREE-BODY PROBLEMS ON THE LINE

The algebraic methods of supersymmetric quantum mechanics are used to construct isospectral Hamiltonians for the three-particle Calogero problem [F. Calogero, J. Math. Phys. 10, 2191 (1969)]. The similarity and points of contrast of the present study with the corresponding two-body problem are discussed. It is found that the family of isospectral interactions is determined essentially by the angular part of the potential in the basic Hamiltonian. A case study is presented to investigate the nature of the individual member in the family.

Optical theorem and Aharonov-Bohm scattering

A rigorous derivation of the optical theorem (OT) from the conservation of probability flux (CPF) is presented for scattering on an arbitrary spherically symmetric potential inN-spatial dimensions (ND). The constructed expression for the OT is found to yield the corresponding well-known results for two- and three-dimensional cases in a rather natural way. The Aharonov-Bohm (AB) effect is considered as a scattering event of an electron by a magnetic field confined in an infinitely long shielded solenoid and a similar derivation is attempted for an appropriate optical theorem. Our current understanding of the scattering theory is found to be inadequate for the purpose. The reason for this is discussed in some detail.